Existence and uniqueness of Monge minimizers for a Multi-marginal Optimal Transport problem with intermolecular interactions cost

2024/01/15 by Augusto Gerolin, Gerolin, Augusto, Mircea Petrache +3
Mathematics · #35-XX #49-XX #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2401.07880

openalex publication_date 2024/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate a new multi-marginal optimal transport problem arising from a dissociation model in the Strong Interaction Limit of Density Functional Theory. In this short note, we introduce such dissociation model, the corresponding optimal transport problem as well as show preliminary results on the existence and uniqueness of Monge solutions assuming absolute continuity of at least two of the marginals. Finally, we show that such marginal regularity conditions are necessary for the existence of an unique Monge solution.

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